By default, Excel will pull the two pivot tables from the same pivot cache. Grouping by a date field will be applied to the pivot cache and will affect all pivot tables that are drawn from that pivot cache.

To create a pivot table that is independent of the first pivot table, you need to use the pivot table wizard. You can use the keyboard shortcut Alt-D-P to start the pivot table wizard. You may get a warning about existing pivot tables and saving memory by using existing pivot tables. That is where you need to tell Excel that you want to create a new pivot table. If you click "No" the new pivot table will use a different pivot cache and you can create different groupings on that pivot table.

Be aware that for large data sets this will have an impact on the workbook size and memory, because both pivot caches will be loaded into the memory.